Math Video | Calculus Lesson | Differential Calculus 426

Author

centerofmath

Title

9: The Exponential Function

Video Description

Full-length video lecture by David B. Massey. In this video, we will define the exponential function, exp, one of the most important functions in all of mathematics, and we will derive many of its properties. What we will show is that there exists a number e, which is approximately 2.718, such that the exponential function exp(x) = ex is its own derivative, i.e., (ex)′ = ex. However, it is not so easy to show that such a number e exists. In fact, we will define the function exp first, then define the number e to be exp(1), and then show that exp(x) = ex. Of course, this just pushes back the question to: how do we define exp? There are many approaches to defining exp. The approach that we shall take is that exp is a limit of special polynomial functions. This limit is similar to the real limits that we have looked at, but is slightly different; we will need limits of sequences.

Video Keywords

Differential Calculus, Center of Math, David B. Massey, Calc 1, Exponential Function, Single-Variable Calculus

Category